Drilling Fluid Rheology: Models, Measurements and Hydraulics

Drilling fluid rheology describes how a mud's shear stress changes with shear rate, time and temperature, and the field reads it on a rotational viscometer whose 600 r/min speed shears the sample at 1,022 s-1. Every circulating drilling fluid needs that curve to carry cuttings, suspend solids at rest and keep pump pressure inside the limits of the hole.

Three models turn dial readings into hydraulics inputs: Bingham plastic, power law and Herschel-Bulkley. API RP 13D (8th edition, April 2026) is the current practice for these calculations.

One illustrative reading set gives a Bingham yield point of 20 lbf/100 ft2 (9.58 Pa) but a Herschel-Bulkley yield stress of 6 lbf/100 ft2 (2.87 Pa), the 0.30 ratio published for water-based mud. Cold, heat and contamination each push the curve out of range.

Standards and regulations are checked against their issuing bodies, product values against the named data sheet and figures against the dated source named in the sentence; see our methodology and fact-checking.

What Is Drilling Fluid Rheology?#

Drilling fluid rheology is the study of how the fluid flows as a function of shear rate, time and orientation, reported as dial readings, plastic viscosity, yield point, gels and model parameters at a stated temperature.

Rheology matters because one mud works at three shear rates: it lifts cuttings up the annulus, sets the frictional pressure loss the pumps overcome, and holds solids when circulation stops. Among the drilling fluid properties, rheology links fluid design to hole cleaning and bottomhole pressure.

Is rheology the same as viscosity?#

No, viscosity is one ratio of shear stress to shear rate at one speed, while rheology is the whole stress against shear-rate curve plus its change with time and temperature. Apparent viscosity, for example, is half the 600 r/min dial reading in centipoise, and two muds with equal apparent viscosity can carry very different yield points.

Shear rate, shear stress and their units#

Shear rate is set by rotor speed, 1.7023 s-1 per r/min on the standard rotor-bob, and shear stress by dial deflection, 1.067 lbf/100 ft2 (0.511 Pa) per degree.

Field practice treats one dial unit as one lbf/100 ft2. The table below lists each rheology quantity with its oilfield and SI units and conversion.

Which Rheological Models Describe Drilling Fluids?#

Three rheological models describe drilling fluids in field use: the Bingham plastic model, the power-law model and the Herschel-Bulkley model, which adds a yield stress to the power law (Jachnik, Annual Transactions of the Nordic Rheology Society, 2003).

The same paper records Herschel-Bulkley and Robertson-Stiff in wide use since the late 1980s. The table below states each model form and the units of its parameters.

Bingham plastic model#

The Bingham plastic model treats the fluid as a straight stress line above a yield point, with plastic viscosity as the slope, characterized between 511 and 1,022 s-1 (API RP 13D, 2003 edition).

The IADC Drilling Manual states that the Bingham yield point overestimates the real yield stress and low-shear stresses of most drilling fluids. The 600 and 300 r/min readings alone give the Bingham pair of plastic viscosity and yield point.

Power-law model#

The power-law model describes shear-thinning muds with a flow behavior index n below 1 and a consistency index K, and it entered field use in the late 1960s for xanthan-treated polymer muds (Jachnik 2003).

Polymer water-based muds fit the power law better than the Bingham line. The 2003 edition of API RP 13D fits the model twice, the pipe constants from the 600 and 300 r/min readings and the annulus constants from the 100 and 3 r/min readings, so each pair covers its own flow path.

Herschel-Bulkley model#

The Herschel-Bulkley model adds a yield stress to the power law, and the IADC Drilling Manual recommends it because the Bingham yield point overstates the stress at low shear.

The field method cited from the 5th edition of API RP 13D (2006) estimates that yield stress from the 6 and 3 r/min readings, then fits n and K to the 600 and 300 r/min readings. In AADE-03-NTCE-35 (2003), curve-fit yield stress averaged 0.57 of the Bingham yield point in synthetic-based mud, 0.50 in oil-based mud and 0.30 in water-based mud, inside an acceptable range of 0 to 1.

Worked example: three rheology models on one reading set#

One illustrative reading set at 120 degF (48.9 degC), 60, 40, 32, 22, 8 and 7 dial units at 600, 300, 200, 100, 6 and 3 r/min, gives a Bingham yield point of 20 lbf/100 ft2 (9.58 Pa).

The same six readings give a Herschel-Bulkley yield stress of only 6 lbf/100 ft2 (2.87 Pa). The table below compares each model's fitted parameters and predicted readings with the measured values.

Calculated from illustrative readings, not a field sample; predictions in dial units.

The yield stress of 6 lbf/100 ft2 is 0.30 of the Bingham yield point, equal to the AADE water-based mud average. The pipe fit misses the low end and the annulus fit the high end. Any other reading set runs through the same three models in the rheology calculator.

How Is Rheology Measured on a Viscometer?#

Rheology is measured on a rotational coaxial-cylinder viscometer that turns an outer rotor around a bob across a 0.046 in (1.17 mm) gap and reads the torque on the bob as a dial deflection at set speeds.

Water-based muds are tested to API RP 13B-1 (6th edition, January 2026) and nonaqueous muds to API RP 13B-2 (6th edition, July 2023, with Addendum 1 of April 2025). Calculations follow API RP 13D (8th edition, April 2026), which replaced the 7th edition, September 2017, reaffirmed 2023, superseded 2026.

The Marsh funnel gives one flow time, not a curve: 1 US quart (946 mL) of fresh water drains in 26 +/- 0.5 s, and mud is reported in s/qt. Model fitting therefore needs viscometer readings at 600, 300, 6 and 3 r/min.

Test temperature and reporting#

Rheology is reported at 120 degF (48.9 degC) for most wells and 150 degF (65.6 degC) for high-temperature wells (IADC Drilling Manual), so a reading without its temperature cannot be compared.

Deepwater programs add a cold check at mudline temperature (Drilling Contractor, 2003). The daily mud report records rheology next to the solids analysis and hydraulics, as the AADE guide to the daily mud report lists them.

Target Rheology by Fluid System and Hole Section#

Rheology targets are set in each well's mud program rather than by a standard, and published values cluster by application, as the table below shows.

The table lists published rheology targets and design conditions with their sources.

Published examples, not limits; each well's mud program sets its own values.

Field data add a trend rather than a target: across 48,310 mud reports, yield point ran higher at lower mud weights and lower at higher mud weights (AADE-03-NTCE-35, 2003).

What Raises and Lowers Rheology: Viscosifiers, Thinners and Solids#

Rheology rises with viscosifiers, drilled and added solids, flocculation and cold, and falls with thinners, dilution, solids removal and heat, so a mud engineer adjusts it with additive classes rather than one material.

Clays and polymers among the drilling fluid viscosifiers, such as bentonite and xanthan gum, raise it. Plastic viscosity follows the solids concentration and the base-liquid viscosity (IADC Drilling Manual). Yield point follows the clay state: freshly dispersed clay or lime raises it, and a deflocculant in a clay-based mud lowers it. The table below compares how each additive or action changes rheology.

Qualitative effects; doses sit on each material page.

Temperature and pressure effects#

Water-based and oil-based mud viscosity rises exponentially as temperature falls (Offshore magazine), and pressure has an appreciable effect on oil-based fluids but a negligible one on water-based fluids (API RP 13D, 2003 edition).

The same Offshore magazine report gives mudline conditions of 35.6 degF (2 degC) and up to 5,802 psi (400 bar) as not uncommon. Heat degrades viscosifiers instead. Lab attapulgite suspensions of 2 to 8 % by mass lost 72 to 92 % of their 104 degF (40 degC) viscosity at 428 degF (220 degC) (Scientific Reports, 2025). Organo-sepiolite oil fluids lose rheology above 356 degF (180 degC), per a peer-reviewed review. Xanthan, guar, diutan, mixed metal hydroxide and PHPA degrade almost totally over extended time at 300 degF (148.9 degC) (Tuttle and Listi, GRC Transactions 40, 2016).

Flat rheology for cold deepwater risers#

Flat rheology means yield point, 6 and 3 r/min readings and gels stay relatively constant over a wide temperature and pressure range, as synthetic-based mud needs from a 40 degF (4.4 degC) mudline to a 150 degF (65.6 degC) check.

Drilling Contractor (2003) gives those two design temperatures, and the landmark flat-rheology paper is Fimreite et al. (SPE-87128-MS, 2004). A flat profile keeps circulating pressure predictable at both ends, the design target of deepwater drilling fluids in long risers.

How Rheology Drives Hydraulics and Circulating Density#

Rheology drives hydraulics because the stress a mud needs to flow at the shear rates of the drill pipe and annulus sets the frictional pressure loss, and the annular part of that loss raises bottomhole circulating density.

The 2003 edition of API RP 13D treats single-phase liquid flow without temperature or compressibility effects on density. In deepwater wells cold seawater raises rheology in the riser, which makes circulating density the main concern where fracture gradients are low (AADE).

Annular pressure loss, expressed as a mud weight over true vertical depth and added to the static mud weight, gives the equivalent circulating density at the bit.

Laminar and turbulent flow in pipe and annulus#

Flow stays laminar up to a Reynolds number of about 2,100 and passes through a transition between 2,000 and 4,000 (API RP 13D, 2003 edition), and laminar annular flow has wall shear rates below 100 s-1 (Jachnik 2003).

Those rates put the annulus at the low end of the viscometer and the drill pipe at the high end. The table below maps each viscometer speed and flow path to its shear rate.

Windows as published in API RP 13D rheology and hydraulics, 2003 edition.

Problems When Rheology Is Out of Range: Losses, Settling and Contamination#

Rheology out of range shows up as pressure, cuttings or chemistry problems: high readings raise annular pressure loss, low 6 and 3 r/min readings let solids settle, and a rising yield point signals contamination.

The five signals and their cause are listed below.

• High plastic viscosity: excess drilled solids or a viscous base fluid; dilution and solids removal lower it.
• Low 6 and 3 r/min readings: cuttings concentration rises as yield point falls and plastic viscosity rises (Busahmin et al., OALib Journal, 2017), which hurts hole cleaning, and weighting material settles as barite sag.
• Rising yield point and progressive gels with Mf rising faster than Pf: carbonate drilling fluid contamination, where deflocculants have little effect and lime or gypsum treats it (AADE).
• Cold-water rise in annular rheology: higher circulating density in deepwater wells.
• Viscosity loss at temperature: biopolymer degradation at 300 degF (148.9 degC) in geothermal drilling fluids.

Excess yield point and plastic viscosity raise annular pressure loss, and where the formation has a low fracture gradient that added pressure leads to lost circulation.

Where Rheology Sits Among Drilling Fluid Properties#

Rheology is one of five property families of a drilling fluid, next to density, filtration, solids and chemistry, and its low-shear end connects it to gels, suspension and sag.

The rheology of completion and workover fluids is a separate field. The rheology of well-cementing slurries is a separate field as well.

Gels and low-shear readings#

Gel strength is the maximum 3 r/min reading after 10 s and 10 min of rest, the time-dependent part of rheology that plain dial readings at speed do not show.

Two muds with equal readings while circulating can build different gels at rest. The four neighboring rheology properties are listed below.

• Gel strength: the 10 s and 10 min readings at 3 r/min.
• Low-shear-rate viscosity: the suspension end of the curve, measured on a Brookfield viscometer.
• PV and YP: the Bingham values from the 600 and 300 r/min readings.
• The drilling fluid properties family: density, rheology, filtration, solids and chemistry.